Chosen Solution
My son used my PSP, then he wanted to charge it up, but he used another charger. The PSP Charger is a 5V 1500mA, the other one is 19V, 1.58A My kid said that he plugged the psp with the other charger (a notebook one) and it lasted about a second, then it went off. No LED, no charge, no nothing.
PepeGrillo, the very first thing you could do, is to open it up. The guides for that are here. Check for any obvious damage, like burnt or charred components. There is a power fuse on the motherboard that may have blown. Check this video for more information. Hope this helps, good luck.